A mixture has lots of different elements that are not necessarily bonded to each other, like sea water has lots of dirt, animals, and plant parts in it. Compared to a solution (strictly salt and water, which bond and ionize with each other).
The balanced molecular chemical equation for the reaction is (NH4)2SO4(aq) + FeCl2(aq) -------> FeSO4(aq) + 2NH4Cl(aq).
The rule for writing a balanced chemical reaction equation is that the number of atom of each element on the right hand side must be the same as the number of atoms of the same element on the left hand side of the reaction equation. This is achieved by performing an atom count.
The balanced molecular chemical equation for the reaction in aqueous solution for ammonium sulfate and iron(II) chloride is;
(NH4)2SO4(aq) + FeCl2(aq) -------> FeSO4(aq) + 2NH4Cl(aq)
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FeCl₂ + 2NH₄OH → Fe(OH)₂ + 2NH₄Cl